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A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems

RELIABILITY ENGINEERING & SYSTEM SAFETY 2015年第Oct.期142卷 221-230页

作者： Huang, Chia-Ling Kainan Univ Dept Logist & Shipping Management Taoyuan 33857 Taiwan

This paper proposes a new swarm intelligence method known as the Particle-based Simplified Swarm Optimization (PSSO) algorithm while undertaking a modification of the Updating Mechanism (UM), called N-UM and R-UM, and simultaneously applying an Orthogonal Array Test (OA) to solve reliability-redundancy allocation problems (RRAPs) successfully. One difficulty of RRAP is the need to maximize system reliability in cases where the number of redundant components and the reliability of corresponding components in each subsystem are simultaneously decided with nonlinear constraints. In this paper, four REAP benchmarks are used to display the applicability of the proposed PSSO that advances the strengths of both PSO and SSO to enable optimizing the RRAP that belongs to mixed-integer nonlinear programming. When the computational results are compared with those of previously developed algorithms in existing literature, the findings indicate that the proposed PSSO is highly competitive and performs well. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Reliability Redundancy allocation problem PSO SSO mixed-integer nonlinear programming

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The Steiner travelling salesman problem with correlated costs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第1期245卷 62-69页

作者： Letchford, Adam N. Nasiri, Saeideh D. Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Lancaster Dept Math & Stat Lancaster LA1 4YX England

The Steiner Travelling Salesman Problem (STSP) is a variant of the TSP that is suitable for instances defined on road networks. We consider an extension of the STSP in which the road traversal costs are both stochastic and correlated. This happens, for example, when vehicles are prone to delays due to rush hours, road Works or accidents. Following the work of Markowitz on portfolio selection, we model this problem as a bi-objettive mean-variance problem. Then, we show how to approximate the efficient frontier via integer programming. We also show how to exploit certain special structures in the correlation matrices. Computational results indicate that our approach is viable for instances with up to 100 nodes. It turns out that minimum variance tours can look rather different from minimum expected cost tours. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Travelling salesman problem Mean-variance optimisation mixed-integer nonlinear programming

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Continuous Piecewise Linear Delta-Approximations for Bivariate and Multivariate Functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第1期167卷 102-117页

作者： Rebennack, Steffen Kallrath, Josef Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Univ Florida Dept Astron Gainesville FL 32611 USA BASF SE Sci Comp D-67056 Ludwigshafen Germany

For functions depending on two variables, we automatically construct triangulations subject to the condition that the continuous, piecewise linear approximation, under-, or overestimation, never deviates more than a given -tolerance from the original function over a given domain. This tolerance is ensured by solving subproblems over each triangle to global optimality. The continuous, piecewise linear approximators, under-, and overestimators, involve shift variables at the vertices of the triangles leading to a small number of triangles while still ensuring continuity over the entire domain. For functions depending on more than two variables, we provide appropriate transformations and substitutions, which allow the use of one- or two-dimensional -approximators. We address the problem of error propagation when using these dimensionality reduction routines. We discuss and analyze the trade-off between one-dimensional (1D) and two-dimensional (2D) approaches, and we demonstrate the numerical behavior of our approach on nine bivariate functions for five different -tolerances.

关键词： Global optimization nonlinear programming mixed-integer nonlinear programming Nonconvex optimization Error propagation

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Cutting planes for RLT relaxations of mixed 0-1 polynomial programs

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MATHEMATICAL programming 2015年第2期151卷 639-658页

作者： Fomeni, Franklin Djeumou Kaparis, Konstantinos Letchford, Adam N. Univ Lancaster Sch Management Dept Management Sci Lancaster LA1 4YX England

The reformulation-linearization technique, due to Sherali and Adams, can be used to construct hierarchies of linear programming relaxations of mixed 0-1 polynomial programs. As one moves up the hierarchy, the relaxations grow stronger, but the number of variables increases exponentially. We present a procedure that generates cutting planes at any given level of the hierarchy, by optimally weakening linear inequalities that are valid at any given higher level. Computational experiments, conducted on instances of the quadratic knapsack problem, indicate that the cutting planes can close a significant proportion of the integrality gap.

关键词： Polynomial optimisation Cutting planes mixed-integer nonlinear programming Quadratic knapsack problem

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A nonlinear model for a capacitated random transportation network

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2015年第8期32卷 500-515页

作者： Shiripour, Saber Mahdavi-Amiri, Nezam Mahdavi, Iraj Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Sharif Univ Technol Fac Math Sci Tehran Iran

In this study, we consider a capacitated location-multi-allocation-routing problem with population-dependent random travel times. The objective is to find appropriate locations as server locations among the candidate locations, allocate the existing population in each demand node to server locations, and determine the movement path of each member to reach its corresponding server with respect to the simultaneous change of the random travel times so that the expected total transportation time is minimized. In our study, the concept of population-dependent random travel times incurs two issues: (1) consideration of some random factors in computing the travel times and (2) impact of the traveling population (presence of people or vehicles) on these random factors simultaneously. Here, three random factors of the time spent in traffic, the number of accidents, and the number of road failures are considered. Also, the capacities of server nodes for servicing the people or vehicles and the capacities of arcs to pass the people or vehicles are assumed to be limited. Defining a linear function for population-dependent random travel time, we formulate the problem as a mixed-integer nonlinear programming model. Also, to investigate the validation and behavior of the proposed random model, several network examples are provided and computational results are analyzed.

关键词： population-dependent random travel times multi-allocation Poisson distribution function mixed-integer nonlinear programming

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Continuous Piecewise Linear Delta-Approximations for Univariate Functions: Computing Minimal Breakpoint Systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第2期167卷 617-643页

作者： Rebennack, Steffen Kallrath, Josef Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Univ Florida Dept Astron Gainesville FL 32611 USA BASF SE Sci Comp GMC MS B009 D-67056 Ludwigshafen Germany

For univariate functions, we compute optimal breakpoint systems subject to the condition that the piecewise linear approximator, under-, and over-estimator never deviate more than a given -tolerance from the original function over a given finite interval. The linear approximators, under-, and over-estimators involve shift variables at the breakpoints allowing for the computation of an optimal piecewise linear, continuous approximator, under-, and over-estimator. We develop three non-convex optimization models: two yield the minimal number of breakpoints, and another in which, for a fixed number of breakpoints, the breakpoints are placed such that the maximal deviation is minimized. Alternatively, we use two heuristics which compute the breakpoints subsequently, solving small non-convex problems. We present computational results for 10 univariate functions. Our approach computes breakpoint systems with up to one order of magnitude less breakpoints compared to an equidistant approach.

关键词： Global optimization nonlinear programming mixed-integer nonlinear programming Non-convex optimization

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An algorithm for two-stage stochastic mixed-integer nonlinear convex problems

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ANNALS OF OPERATIONS RESEARCH 2015年第1期235卷 581-598页

作者： Mijangos, E. Univ Basque Country UPV EHU Dept Appl Math & Stat & Operat Res Bilbao Spain

We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0-1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes.

关键词： Stochastic programming Convex programming Branch-and-fix coordination method mixed-integer nonlinear programming Quadratic programming Outer approximation

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A primal heuristic for optimizing the topology of gas networks based on dual information

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2015年第1期3卷 53-78页

作者： Humpola, Jesco Fuegenschuh, Armin Lehmann, Thomas Zuse Inst Berlin D-14195 Berlin Germany Univ Fed Armed Forces Hamburg Helmut Schmidt Univ D-22043 Hamburg Germany

We present a novel heuristic to identify feasible solutions of amixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP.

关键词： mixed-integer nonlinear programming Relaxations Heuristics Duality nonlinear network design applications

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Solving reliability redundancy allocation problems with orthogonal simplified swarm optimization

Solving reliability redundancy allocation problems with orth...

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International Joint Conference on Neural Networks (IJCNN)

作者： Yeh, Wei-Chang Jiang, Yun-Zhi Chung, Vera Yuk Ying He, Xiangjian Natl Tsing Hua Univ Dept Ind Engn & Engn Managemen Hsinchu 300 Taiwan Jiangxi Agr Univ Sch Software Nanchang 330045 Peoples R China S China Univ Technol Sch Software Engn Guangzhou 510006 Guangdong Peoples R China Univ Sydney Sch Informat Technol Sydney NSW 2006 Australia Univ Technol Sydney Comp Vis & Recognit Lab Res Ctr Innovat IT Serv & Applicat iNEXT Broadway NSW 2007 Australia

ISBN: (纸本)9781479919598

This study applies a penalty guided strategy and the orthogonal array test (OA) based on the Simplified Swarm Optimization algorithm (SSO) to solve the reliability redundancy allocation problems (RRAP) in the series system, the series-parallel system, the complex (bridge) system, and the overspeed protection of gas turbine system. For several decades, the RRAP has been one of the most well known techniques. The maximization of system reliability, the number of redundant components, and the reliability of corresponding components in each subsystem have to be decided simultaneously with nonlinear constraints, acting as one difficulty for the use of the RRAP. In other words, the objective function of the RRAP is the mixed-integer programming problem with the nonlinear constraints. The RRAP is of the class of NP-hard. Hence, in this paper, the SSO algorithm is proposed to solve the RRAP and improve computation efficiency for these NP-hard problems. There are four RRAP problems used to illustrate the applicability and the effectiveness of the SSO. The experimental results are compared with previously developed algorithms in literature. Moreover, the maximum-possible-improvement (MPI) is used to measure the amount of improvement of the solution found by the SSO to the previous solutions. According to the results, the system reliabilities obtained by the proposed SSO for the four RRAP problems are as well as or better than the previously best-known solutions.

关键词： Reliability Redundancy allocation problem RRAP Simplified Swarm Optimization algorithm SSO mixed-integer nonlinear programming

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Discrete flow pooling problems in coal supply chains 21

Discrete flow pooling problems in coal supply chains

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21st International Congress on Modelling and Simulation (MODSIM) held jointly with the 23rd National Conference of the Australian-Society-for-Operations-Research / DSTO led Defence Operations Research Symposium (DORS

作者： Boland, N. Kalinowski, T. Rigterink, F. Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Newcastle Sch Math & Phys Sci Callaghan NSW Australia

ISBN: (纸本)9780987214355

The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate pools and outputs so as to satisfy requirements on the output qualities. The blending in two stages (in pools and outputs) introduces bilinear constraints. The pooling problem can alternatively be described as a minimum cost network flow problem with additional bilinear constraints to capture the blending of raw materials. In this paper we study a variation of the pooling problem that arises naturally in the coal mining industry and is sometimes referred to as grade targeting. Coal is made-to-order according to customers' desired product qualities. Deviations from these target qualities result in contractually agreed bonuses and penalties. In the pooling problem variation we study, costs are associated with these bonuses and penalties instead of network flows. While in the original pooling problem we have hard bounds on the qualities and unmet demand is penalised in the objective function, in our coal mining variation we have hard demand constraints and deviations from target qualities are penalised. This makes finding a feasible solution easy, while in the pooling problem finding a nontrivial feasible solution that satisfies the quality requirements is already hard. An implication of this is that we are able to solve larger problem instances than those typically studied in the pooling problem literature. To model the coal blending process accurately, we define a time-expanded network where the intermediate pools represent coal stockpiles over time. Since coal is transported in large quantities, we study the trade-off between continuous and discretized flows in coal blending, i.e., solving a continuous flow prob

关键词： Coal blending pooling problem mixed-integer nonlinear programming mixed-integer linear programming

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